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Mathematics > Numerical Analysis
Title: Fractional Newton-Raphson Method and Some Variants for the Solution of Non-linear Systems
(Submitted on 5 Aug 2019 (v1), last revised 24 Mar 2020 (this version, v6))
Abstract: The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions. The origin of these methods is the fractional Newton-Raphson method but unlike the latter, the orders of fractional derivatives proposed here are functions. In the first method, a function is used to guarantee an order of convergence (at least) quadratic, and in the others, a function is used to avoid the discontinuity that is generated when the fractional derivative of the constants is used, and with this, it is possible that the methods have at most an order of convergence (at least) linear.
Submission history
From: Anthony Torres [view email][v1] Mon, 5 Aug 2019 03:22:37 GMT (185kb,D)
[v2] Tue, 6 Aug 2019 00:52:22 GMT (185kb,D)
[v3] Mon, 7 Oct 2019 22:21:54 GMT (186kb,D)
[v4] Tue, 29 Oct 2019 00:57:47 GMT (186kb,D)
[v5] Sat, 7 Mar 2020 04:41:31 GMT (715kb,D)
[v6] Tue, 24 Mar 2020 22:16:35 GMT (715kb,D)
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